Of course, the "basis" in the story line are related and the event succession is also related. This article made it clearer to me. However, it's not a Bioshock game in the sense of "being in the same universe" (rapture reality).
Thanks for the article by the way.

Believe it or not, one theory that I've heard of is that infinite is actually Bioshock 1 (or maybe even 2) set in an alternate reality. Remembering how Elizabeth could travel through time (and as a result, realities) Comstock is simply Ryan, and Columbia is simply Rapture in another reality. One piece of evidence is how Booker was able to use the bathysphere, even though only people in the same genetic pool as Ryan could.

I didn't hear of that theory but I've also thought of that. As you pointed out, since Elizabeth can travel between realities, they could reach to an alternate reality (Bioshock's reality) from Infinite's.

I'm not saying it was a bad game, I'm just unsure with the sort of vibe the game was trying to give across, in B1 it was lonlyness, in infinite it was being hunted, but in B2 I couldn't understand what it was giving across, which is what put me off.